Spurs recently surrendered a 10-point gap to North London rivals Arsenal, who now find themselves three points clear of the Lilywhites with eight games to go.
Redknapp's side appear to have the easier run-in compared to the Gunners, and the veteran tactician has laughed off any suggestion that third place may be out of reach.
"No, it's not out of reach, of course not," he said. "I still think we'll finish above Arsenal - bring it on, Arsene! [Wenger].
"The position we were in a month ago, we looked nailed on, didn't we?
"It would be a bigger blow if we don't make it, that's for sure. That would knock me for six."
Spurs are hoping to secure Champions League football for just the second time in their history and Redknapp believes it to be a tougher task this season.
"Man City are now established as a certainty, Man United are a certainty, Arsenal have been there every year, Chelsea, Liverpool are going to get stronger," he added.
"You'd have thought if you can make it this year, it's going to be even harder.
"I enjoyed it last year. It was new to me, it wasn't something that I've had. It's not been part of my life any more than it's been part of Tottenham's life.
"They've not been used to Champions League, so it wasn't suddenly: 'Oh my God, we've not got Champions League."
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